# Carlos Di Prisco: Chromatic numbers of Borel graphs

Place: Fields Institute (Room 332)

Date: March 28, 2018 (13:30-15:00)

Speaker: Carlos Di Prisco

Title: Chromatic numbers of Borel graphs

Abstract: A graph G=(X, R) defined on a Polish space X is Borel if the binary relation R is a Borel subset of the cartesian product of X with itself.
The Borel chromatic number of such a graph is the least cardinal k such that there is a Borel measurable function c from X to k coloring of the graph, that is, connected elements of X get different images under c.
The study of Borel chromatic numbers was initiated by Kechris, Solecki and Todorcevic (Advances in Mathematics 141 (1999) 1-44) and has received considerable attention since then.
We will survey some of the basic results regarding this concept and mention some open questions.